Total positivity of the cubic trigonometric Bézier basis
type: Item
instance of: scholarly article
title: Total positivity of the cubic trigonometric Bézier basis
zbMATH Open document ID: 1406.65011
DOI: 10.1155/2014/198745
author: Yuanpeng Zhu
author: Xuli Han
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters \(\lambda\) and \(\mu\) given in [the first author et al., Appl. Math. Lett. 22, No. 2, 226--231 (2009; Zbl 1163.65307)] forms an optimal normalized totally positive basis for \(\lambda,\mu\in(-2,1]\). Moreover, we show that for \(\lambda=-2\) or \(\mu=-2\) the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 7010568
Wikidata QID: Q59050237
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/198745
OpenAlex ID: W2004003062
DBLP publication ID: journals/jam/HanZ14
description: scientific article; zbMATH DE number 7010568